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Record Nr. |
UNINA9910813457003321 |
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Titolo |
Computational prospects of infinity . Part I Tutorials / / editors, Chitat Chong ... [et al.] |
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Pubbl/distr/stampa |
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Singapore ; ; Hackensack, NJ, : World Scientific, c2008 |
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ISBN |
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1-281-93434-8 |
9786611934347 |
981-279-405-0 |
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Edizione |
[1st ed.] |
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Descrizione fisica |
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1 online resource (264 p.) |
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Collana |
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Lecture notes series / Institute for Mathematical Sciences, National University of Singapore ; ; v. 14 |
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Altri autori (Persone) |
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ChongC.-T <1949-> (Chi-Tat) |
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Disciplina |
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Soggetti |
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Recursion theory |
Set theory |
Infinite |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references. |
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Nota di contenuto |
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CONTENTS; Foreword; Preface; Recursion Theory Tutorials; Five Lectures on Algorithmic Randomness Rod Downey; 1. Introduction; 2. Lecture 1: Kolmogorov complexity basics; 2.1. Plain complexity; 2.2. Symmetry of Information; 2.3. Pre.x-free complexity; 2.4. The Coding Theorem; 2.5. Pre.x-free symmetry of information; 2.6. Pre.x-free randomness; 2.7. The overgraph functions; 3. Lecture 2: Randomness for reals; 3.1. Martin-L ̈of randomness; 3.2. Schnorr's Theorem and the computational paradigm; 3.3. Martingales and the prediction paradigm; 3.4. Super martingales and continuous semimeasures |
3.5. Schnorr and computable randomness 4. Lecture 3: Randomness in general; 4.1. The de Leeuw, Moore, Shannon, Shapiro Theorem, and Sacks' Theorem; 4.2. Coding into randoms; 4.3. Kucera Coding; 4.4. n-randomness; 4.5. Notes on 2-randoms; 4.6. Kucera strikes again; 4.7. van Lambalgen's Theorem; 4.8. Effective 0-1 Laws; 4.9. Omega operators; 5. Lecture 4: Calibrating randomness; 5.1. Measures of relative randomness and the Kucera-Slaman Theorem; 5.2. The Density Theorem; 5.3. Other measures of relative randomness; 5.4. <C and <K.; 5.5. Outside of the randoms; 5.6. |
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